Contoured ultrasonic delay line

ABSTRACT

A delay line comprising a strip of ultrasonic solid material having a pair of elongated and generally convex major surfaces to form a contoured cross section. Acoustic wave propagation between the major surfaces is confined to a region which extends a distance A in both directions from the center of the strip along the width or transverse dimension, where A is less than one-half of the width and is a function of the acoustical wavelength.

United States Patent [1 Whitney et al.

CONTOURED ULTRASONIC DELAY LINE Inventors: David J. Whitney, Amherst;

Raymond R. Nepveu, Londonderry, both of N.l-l.; Walter W. Gerlach, Westford, Mass.

Sanders Associates, Inc., Nashua; N H.

Filed: June 14, 1973 Appl. No.: 370,196

Assignee:

US. Cl 333/30 R Int. Cl. H03h 9/26, H03h 9/30 Field of Search 333/30 R, 30 M, 72;

References Cited UNITED STATES PATENTS 3,041,556 6/1962 Meitzler ..333/30R ea-qa-i-q [451 Apr. 23, 1974 Primary Examiner-Archie R. Borchelt Assistant Examiner-Marvin Nussbaum Attorney, Agent, or Firm-Louis Etlinger; Seligman, Richard I.

[ ABSTRACT 8 Claims, 10 Drawing Figures TERTHHEIIJAPR23 2914 3806840 SHEET 1 HF 3 l 1 l o 0.05 0.30 0.15

FREQUENCY-THICKNESS PRODUCT (f.h)

PATENTEBAPR 23 1974 SHEET 3 0F 3 ihz Ilullll.

FIG?

FIGES FIGIO CONTOURED ULTRASONIC DELAY LINE BACKGROUND OF THE INVENTION A. Field of the Invention This invention relates to delay devices and in particular to solid ultrasonic delay lines.

Ultrasonic delay lines are generally operable to provide either a nondispersive or a dispersive delay of continuous wave or pulse type signals. The terms dispersive and nondispersive refer to the delay versus frequency characteristic of a delay line. If delay changes with frequency, the line is said to be dispersive. On the other hand, if the delay is constant, or nearly so, for all frequencies, the line is termed nondispersive.

B. Prior Art The propagation of continuous waves in solid plates is described inch apte r of the reference book Me chanical Waveguides by Martin Redwood, Pergamon Press, 1960. This description is based upon the premise that in a uniform thickness sheet of infinite width there is no variation of acoustical particle displacement in the width of y direction. A close approximation of actual performance to this theory has been realized by the application of absorbing tapeto the edges of a finite width metallic strip (e.g., aluminum or aluminum alloy) such that there are no edge reflections'which interlarge amount of acoustic energy is absorbed by the tape, thereby resultingin relatively high acoustic losses.

Acoustic delay lines or waveguides of various cross sections, such as circles, rectangles and elipses, not employing absorbing means along the length thereof, have been studied as exemplified by Chapter 6 of the aforementioned Redwood reference. Dispersive delay lines have also been made of wire as evidenced by the article of IE. May entitled Wire Type Dispersive Ultrasonic Delay Lines, IRE Transactions, Volume UE-7, No. 2, June, 1960. While these delay lines do not suffer the loss due to absorbing tape, other problems have been encountered. For example, the very small area of the piezoelectric transducers on wire type dispersive lines have limited their use to relatively low frequencies. In addition, the interference of unwanted modes of propagation have prevented smooth transmission over a wide band of frequencies.

BRIEF SUM-MARY OF THE INVENTION Briefly, an acoustic delay line embodying the present invention is comprised of a strip of ultrasonic transmismension. A is less than one half of the width and is a function of the acoustical frequency and phase velocity of the acoustic waves. Since the phase velocity characteristics of the undesired modes differ from those of the desired mode, the parameter A is generally larger for the unwanted or spurious propagation modes. By properly positioning the inside edge of the absorbing tape, it is possible to suppress the unwanted modes of propagation.

' BRIEF DESCRIPTION OF THE DRAWING In the accompanying drawings like reference characters denote like elements of structure; and

FIG. 1 is a plan view of a portion of an acoustic delay line embodying the present invention;

FIG. 2 is a cross sectional view taken along the lines 2-2 of the FIG. 1 delay line;

FIG. 3 is a plot of the ratio of phase velocity to transverse velocity versus the frequency and thickness product for an aluminum stripdelay line;

FIG. 4 is a graph showing exemplary contours for delay lines embodying the present invention;

FIG. 5 is aplot of another exemplary contour for a delay line embodying the present invention;

FIG. 6 is a plan view of a portion .of a'contoured delay line which is a further embodiment of the invention;

FIG. 7 is a cross sectional view taken along the lines 77 of FIG. 6;

FIG. 8 is a line graph illustrating the boundaries of wave propagation for different longitudinal modes;

FIG. 9 is a plan view of a portion of another contoured delay line embodiment of the invention; and

FIG. 10 is a cross sectional view of the FIG. 9 embodiment.

DESCRIPTION OF PREFERRED EMBODIMENT Referring now to FIGS. 1 and 2 there is shown a portion of a contoured'delay line 20 embodying the present invention. The length, width and heighth of the line 20 extend in the z, y and x'directions, respectively, which directions are depicted at 21 and 22in FIGS. I and 2, respectively. The width W (FIG. 2) is many times greater than the maximum height along the x direction. Although the line 20 may consist of any'ultrasonic transmission material, it preferably takes the form of an elongated thin strip of aluminum or aluminum alloy. The total length of the'strip is a function of delay required in any desired application. Preferably, the line thickness is tapered throughout the length of the strip so as to enhance the frequency range over which linear dispersive operation occurs.

Conventional piezoelectric ceramic transducers in the form of rectangular bars are bonded to the end faces of the strip, only one of which is shown at 24 in FIG. 1. These transducers are poled in the thickness direction, electroded, and soldered to the line with the poling direction parallel to the length of the strip so as to produce and respond to vibrations in a thicknesslongitudinal-mode. Accordingly, when one of the transducers is excited by an alternating voltage applied to the electroded areas of the major surfaces thereof, a thickness-longitudinal-mode of vibration is induced therein. This vibration in turn produces an elastic wave motion in the strip which propagates down the line. When the propagated energy reaches the transducer at the opposite end, a thickness-longitudinal-mode of vibration is induced therein and converted by the transducer to electrical energy. As will be clear to those skilled in the art, the electrical and physical connections at each of the ends of the line are similar and therefore either transducer can be used as the input or output, i.e., the line is completely reciprocal.

In accordance with the present invention, the strip thickness is given a contour in which the maximum thickness occurs at the center of the strip. In the embodiment illustrated in FIGS. 1 and 2, the contour takes the form of a convex continuous shape in which the maximum thickness occurs at the center line 23 of the strip. Due to the contour, the elastic wave propagation in the z direction is confined to an area which extends a distance A on either side of the center line 23. As best seen in FIG. 2, the reflection angle of an elastic wave between the contoured major surfaces a and 20b is maximum at or near the center line 23 and becomes gradually smaller until at a distance A it becomes zero and reverses itself. That is, the contouring of the major surfaces tends to set up points of reflection at a distance A on either side of the center line 23 so that the propagation of an elastic wave is confined to this region.

As will become apparent thereinafter, the distance A turns out to be smaller for wave propagation in the first longitudinal mode M11 than for propagation in the undesired modes M12, M21 and M22. As a result, the placement of the edges of a pair of absorber tapes and '26 can be chosen so as to suppress wave propagation in the undesired modes.

In the discussion which follows, it is assumed that the x, y and z coordinate axes are superimposed upon the strip 20 so that the center line 23 becomes the x 2 plane. Using a ray method of analysis, assume that two rays, r and r shown in FIG. 1, are symmetrical about the center line 23. These rays travel in three dimensions as follows: (a) move in the x direction by alternate reflection between the major surfaces 20a and 20b of the strip in a manner shown in FIG. 2; (b) progress from side to side of the strip (y direction) as shown in both FIGS. 1 and 2; and (c) have an overall resultant propagation along the length of the strip (2 direction).

The lateral or y position of each ray at any instant of time can be expressed as a sine function of the distance along the strip length or -z direction as follows:

y 5 A sinB z where ,8 2rr/Xl, )rl is the wavelength of the sine wave nated C The pfiaseviacny 'drreaezr along tli s'irip length (z -.axis) is designated C,,. C, also represents the phase velocity of the acoustic wave propagation along the strip.

As the phase front 26 of the ray r moves along the sine curve, the longitudinal phase velocity C is larger than the tangeh'fial phase velocity C55 along the sine curve and is related to it in the following way:

C 9 C cos 0 along a third ray, r be the same as C,,. However, since for r -at the line 2 2, 0 0, C p0 C so that the condit i on is fulfilled. I n other words for constant C C29 must be seaside funetiohore'ifi"aarance with equation (2).

By inspection of the C 8 and Cp vector diagram in FIG. 1, tan 6 dy/dz. The first derivative of equation l) with respect to z is [3A cos ,Bz. From equation (1) sin Bz y/A. Accordingly, tan 0 can be expressed as follows:

From equation (3) it is evident that cos 0 can be expressed as follows:

cos 0= V3 (.42 +1 S ubsti tuting equation (4) into equation(2), the ratio Cp/Cpfi can be expressed as follows:

The mode of propagation described herein is assumed to be symmetrical about the x 2 plane as well as about the y 2 plane. Referring to FIGv 1, this requires that the phase fronts 26 and 27, which intersect at the center line 23 at point 28, be in phase with each other. This requires at y i A that the phase fronts 26 and 27 be separated by n A2, where n is any positive integer and A2 C /f and f is the acoustic frequency.

The analytic formula for the phase front (26 or 27) may be obtained in the following manner. Since, for any value of y, the phase from must be orthogonal to the direction of a ray, the slope of the phase front must be the negative inverse of the slope of the ray. Since the slope of the ray is given by equation (3), the curve zl for the phasefront is given by Assuming that the origin of the coordinate axes 21 coincides with the point 28 in FIG. 1 so that the phase fronts 26 and 27 are symmetrical about the x y plane 5 t 6 and setting y to A in equation (7), the following exhm C n/ CM l/cos sec!) B (A y) pression can be written for 21 (I 4) Z] M M] 7 When the thickness h has its maximum value of h at (8) y=0, equation (14) can be rewritten as follows:

h h 0 V A l Ignoring the minus sign and setting n=1 for the first 0/ A sec B mode, B can be expressed as follows: 5)

2212/0 12 The thickness h at any value of y can be related to the center thickness h as follows:

i h/h h/h h /m, sec (l /sec o Substituting 3: Z'rr/Al into equation (9), M is given by B 0 y A +1 15 (16) M 1r A /A2 Both A and ,B are fractions such that B A is much less than 1 so that terms including A and/or B can be neglected. As a result, the radical expression of The phase velocity of the first and second longitudiv nal acoustic modes in a strip of uniform thickness, h, 20 A2 1 and a radian frequency, w, has been shown in the aforeooh Be simplifi d as follows; mentioned Meeker reference to' be obtainable from a G solution of the following frequency equation: V a 2 E 2 2 4 [44/4 1 2 C" "l2 "f I tan 1 1 .Y 0. 1 A still further approximation of equation 17) can be wh C; 1/2 a??? W RM l M t .7 1 2 C, C, C 1/2 C 2 2 2 2 2 2 I n w C C t C? C; 2 2 2 4 44 2 (n) 1 i In FIG. 3 the curves designated M11 and M12 are (l8) plotted solutions for the first and second longitudinal (symmetric modes) M11 and M12. Also plotted in FIG. Utilizing equations (17) and (18), equation (16) can 3 are curves representing the first and second asymmetbe rewritten as follows:

ric modes M21 and M22. These modes are described andtharreqnency equatians given in charter 5Eift1re h/ho (Ff/2 BzYz/Z 1) (1 32/12) 45 aforementioned Redwood reference. The curves in I 19) FIG. 3 are plotted for Poissons ratio p 0.355, and ff fi s r vlocity C 0Il215iri/ 12sec. Multiplying out the two terms on the right hand side of If Cp in FIG. 3 and in equation (11) is replaced byequation and neglecting terms including 3 and/or C 9, the dependence of C M on thickness for any fre- 5 equation can be Written as follows: quency can be found. Also in FIG. 3 it can be seen that h/h 1 B2 2/2 in the frequency-thickness product range of interest 0 y (0.072 0.105), the curves for the M11 and M22 modes can be closely approximated by the dashed hyperbolic curves 3] and 32, respectively. These approxi- The Percentage reduction from the center thickness mate hyperbolic curves for the M11 and M22 modes o is found from equation (20) to be? may be expressedin equations (12)and (l3) respecwho) zy l00% tivcly, as follows:

- Equations (20) and (2l) basically describe a para- C /f parabolic in shape and independent of the distance A. The percent reduction from the center thickness as l I 5 given by equation (21) is plotted in FIG. 4 for a fre- Umizing h r U Q (12) or equatlon and quency-thickness product of 0.085 MHz inches (the allowing the thickness at y=A to be h, the ratio of h to frequency being equal t9 4 M f values f A can be given y: 0.125, 0.250 and 0.375 inches and corresponding valbolic function such that the contour is approximately ues ofB 1.769, 0.442 and 0.1966, respectively. The points on these curves can be calculated as follows. First, C is calculated from equation 12) by employing a measured value of the transverse velocity C, 0. l 2 l 5 inches/microseconds. Next, the value of B is calculated from equation (9) with the value of k2 being equal to C /f or 0.0434. Then, equation (21) can be employed to calculate different values of the quantity (1h/h 100 percent for different values of y. I-Iaving once selected a value of B, and thus established a desired contour (e.g., one similar to one of the three curves in FIG. 4) at a midband frequency, it is, of course, desirable to find the values of A at the extremes of the frequency range of interest. The value of A for each new wavelength or frequency is then computed directly from equation (9).

With reference again to FIG. 3, two additional or spurious modes M21 and M22 exist in the range of interest. The first asymmetric mode M21 has a positive slope in this range and, hence, is subject to the normal beam spreading loss occurring in a flat or uncontoured delay line strip. However, the reasoning developed above for the M11 mode applies equally to the M22 mode except that the latter mode is asymmetric about the cener y 2 plane. In addition, this mode is closely apprc gimated by the inverse relationship given in equation (13).

In FIG. 5 there is plotted a contour for B 0.268, utilizing equation (21 It is assumed that this contour is to be employed for all sections of a tapered delay line strip, the extreme thicknesses of which are: h 0.0245 and 0.0196 inches. The values of A have been calculated and plotted on the contour for frequency values of 4.3 and 3.7 MHz. for both thickness values in both the M11 and M22 modes, utilizing equations (9), (l2) and (13). By inspection, it can be seen that all the points representing the A values of the spurious mode M22 lie further from the center line than all the points representing the A values of the desired mode M11. It is therefore possible, by positioning the inside edge of the absorbing tapes 25 and 26 (FIGS. 1 and 2) to cover the extremities of the undesired spurious mode (while not covering the extremities of the desired mode), to selectively absorb out the unwanted acoustic wave propagation in the M22 mode. For the example given, the edge of the absorbing tape 25 or 26 should be placed at a distance of about 0.36 inches from the center of the strip for both of the delay line sections.

When different thicknesses are employed to accomplish a more linear delay change over a wider frequency bandwidth, it is possible to change the lateral position of the absorbing tape for different thicknesses of the strip so as to more effectively separate the wanted from the unwanted signals. That. is, the edge of the absorbing tape need not be at the same distance from the center line of the strip for different thicknesses thereof.

The foregoing analysis is heuristic in nature and is not presented as a rigorous treatment of three dimensional wave motions. Experimental results, however, have agreed closely with results predicted from the graphs. Improvements in the continuous wave loss at center frequency of a 4 MHz., 2,500 micro-second aluminum strip dispersive Helay line have bee'fi as much asl 0 decibels as compared to an uncontoured delay line strip of similar design. 7

The'contouring of a delay line strip may be accomplished by etching in from the edges of the strip by laydent a1, it may continue to travel in the edge section ing a loosely coiled delay line strip in an empty tank and filling the tank with the etchant at a slow linear rate up to the center line of the strip. The coil is turned over and the operation repeated for the other edge. In using this technique, the transverse taper produced in one example was 0.0003 inches at plus or minus 0.375 inches from the center of the strip.

It has beenfurther discovered that a workable contour can be achieved by rolling 1.75 inch wide and 0.05 inch thick aluminum strip stock through a two high rolling mill which is set for 40 to 50 percent reduction in thickness of the strip and which has a roll diameter of four inches and an axial roll length of six inches. The contour thus achieved can then be measured and plotted to produce a graph similar to that shown in FIG. 5. The values of ,8 and A can then be calculated for the frequency range of interest.

In other embodiments of the invention, the contour need not be continuous by may have discontinuities.

Thus, the delay line strip portion shown in FIG. 6 has a transverse stepped contour such that the central portion of width Wo has a thickness hl and the two edge sections have a thickness h2 which is smaller than hl. The two edge sections are also covered with absorbing tape 45 and 46.

If a ray of an acoustic wave traveling at a phase velocity C in the strips strikes the step at an angle of inciat a refracted angle a2 and phase velocity C or be totally reflected into the central portion at the angle a1. Snells Law applies in this case as follows:

sin a] CpaI/ IHIZ I ln FlG. 8 the percentage thickness reduction, (1 sin al) percent is plotted on a line graph for two frequencies (3.6 and 4.4 MHZ.) for both the M11 and M22 modes with h1 0.0215 inches. Thus, by control-. ling the thickness ratio h2/h1 (as for example, a reduction of 0.45 percent), the acoustic wave propagation in the desired M11 mode may be guided into the central portion of the strip while the suprious M22 mode wave propagation can be made to excape into the edge sections and be absorbed by the tape.

In FIGS. 9 and 10 there is illustrated a portion of another delay line strip 51 having a further discontinuous type contour embodying the present invention. In this contour, the edges of the strip are reduced with a linear taper leaving a flat width W1 in the center of the strip. This type of contour also includes the case where the width of the flat section W1 is reduced to zero. It should be evident that other contours having curvatures somewhat different from the embodiment shown in FIGS. 1, 2, 6, 7, 9 and 10 may be employed so long What is claimed is:

1. A delay line comprising a strip of ultrasonic transmission materialhaving a pair of elongated and generally convex major surfaces to form a contoured cross section with a and means for applying a beam of acoustic waves to said strip whereby acoustic wave propagation between the major surfaces is confined to a region which extends a distance A in both directions from the center of the strip along the width dimension, where A W/2. 2. A delay line as set forth in claim 1 wherein said beam applying means includes a transducer poled in the longitudinal mode affixed to one end thereof and means for applying electrical signals to said transducer. 3. A delay line as set forth in claim 2 and further including absorbing tape means wrapped around the minor surfaces of said strip and extending inwardly along said major surfaces toward the center of the strip a distance less than W/2 A.

4. A delay line as set forth in claim 2 wherein A is a function of both the acoustical wavecontour is generally continuous.

6. A delay line as set forth in claim 4 wherein said contour includes a central section having a uniform thickness hl and a pair of edge sections each of thickness I12; and

wherein the edges of said absorbing tape means are positioned along the edge sections.

7. A delay line as set forth in claim 4 wherein said contour has a central position of uniform thickness and width W1, where Wl W, and

a pair of tapered edge sections.

8. A delay line asset forth in claim 4 wherein said contour includes a pair of tapered sections which have their maximum thickness at the center of the strip. 

1. A delay line comprising a strip of ultrasonic transmission material having a pair of elongated and generally convex major surfaces to form a contoured cross section with a width W many times greater than the thickness h; and means for applying a beam of acoustic waves to said strip whereby acoustic wave propagation between the major surfaces is confined to a region which extends a distance A in both directions from the center of the strip along the width dimension, where A < W/2.
 2. A delay line as set forth in claim 1 wherein said beam applying means includes a transducer poled in the longitudinal mode affixed to one end thereof and means for applying electrical signals to said transducer.
 3. A delay line as set forth in claim 2 and further including absorbing tape means wrapped around the minor surfaces of said strip and extending inwardly along said major surfaces toward the center of the strip a distance less than W/2 - A.
 4. A delay line as set forth in claim 2 wherein A is a function of both the acoustical wavelength and the acoustical phase velocity such that its values throughout the frequency band of interest are smaller for the longitudinal mode M11 than for the mode M22; and wherein the edges of said absorbing tape means are positioned so as to absorb acoustical wave propagation in the M22 mode and to allow acoustical wave propagation in the M11 mode.
 5. A delay line as set forth in claim 4 wherein said contour is generally continuous.
 6. A delay lIne as set forth in claim 4 wherein said contour includes a central section having a uniform thickness h1 and a pair of edge sections each of thickness h2; and wherein the edges of said absorbing tape means are positioned along the edge sections.
 7. A delay line as set forth in claim 4 wherein said contour has a central position of uniform thickness and width W1, where W1<W, and a pair of tapered edge sections.
 8. A delay line as set forth in claim 4 wherein said contour includes a pair of tapered sections which have their maximum thickness at the center of the strip. 